There are a couple of safety systems used. One is just a diode between the neutral switch wire and the clutch switch wire, the other is a more complicated electronics module. Either way the neutral switch allows starting through the safety unit, the clutch switch directly connects to the solenoid and is the "master" starter enable. If it's the diode kind, replace it (a cheapo commodity diode is fine, don't spring the $$$ for an OEM one); the SSU module is not so easy to repair. Or bypass it and remember not start the motor in gear with clutch engaged.